Aspire Faculty ID #17294 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

$\frac{d}{dx}\left[\int_{0}^{2a} f(\sin 2x)\,dx\right] =$

Solution

Given solution:

$y = e^x (a\cos x + b\sin x)$

Here the solution contains **two arbitrary constants** $a$ and $b$.

The order of a differential equation is equal to the number of arbitrary constants in its general solution.

Therefore,
Observe that the integral

$\int_{0}^{2a} f(\sin 2x)\,dx$

does **not depend on $x$** because the limits are constants.

Hence the entire expression is a constant.

Derivative of a constant is zero.

Therefore,

$\frac{d}{dx}\left[\int_{0}^{2a} f(\sin 2x)\,dx\right] = 0$

Order $=2$

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